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If gravity and acceleration are indistinguishable, then does that mean converting potential energy to kinetic energy generates gravitons... but only temporarily until you stop accelerating?

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    $\begingroup$ The real question here would be (1) whether a free-falling object radiates gravitational waves. If so, then it would presumably be true that (2) those gravitational waves are quantized as gravitons, but we don't have a theory of quantum gravity, so we don't really know. The answer to #1 depends on whether the system has a changing mass quadrupole moment. It is definitely possible to come up with scenarios in which there is acceleration but no gravitational radiation, e.g., two parallel, uniform, infinite sheets of mass. $\endgroup$ – Ben Crowell Oct 2 '14 at 22:34
  • $\begingroup$ Aren't two orbiting bodies both in free fall? These systems are known to generate gravitational waves, so it's certainly possible that freely falling bodies generate gravitational waves. $\endgroup$ – Oscar Cunningham Oct 2 '14 at 22:42
  • $\begingroup$ @OscarCunningham: Yes. The system you describe has a varying mass quadrupole moment, so it radiates. $\endgroup$ – Ben Crowell Oct 2 '14 at 22:43
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    $\begingroup$ There is not even a hint of a sign that gravitons even exist. $\endgroup$ – CuriousOne Oct 3 '14 at 1:48
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    $\begingroup$ @CuriousOne: There are fundamental reasons for thinking that gravitons must exist, because the other fields are quantized, and it's not possible to couple a classical field to a quantum-mechanical field. We simply aren't ever going to detect gravitons directly with any foreseeable technology. $\endgroup$ – Ben Crowell Oct 3 '14 at 1:54
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The criterion for gravitational radiation is (conjectured to be, pending direct evidence) a changing quadrupole moment in the mass distribution, so an accelerating mass distribution does not always radiate, but can do so if the acceleration changes the quadrupole moment. This is in contrast to electromagnetic radiation, which occurs when the charge distribution has a time varying dipole (or higher) moment. An accelerated charge always has a changing dipole moment, so loosely speaking accelerating (classical) charges radiate electromagnetically (in some frame? this rabbit hole is pretty deep).

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    $\begingroup$ conjectured to be, pending direct evidence This is not just a conjecture. It's a firm prediction of GR, already confirmed in quantitative detail by observation of binary pulsars. $\endgroup$ – Ben Crowell Oct 3 '14 at 0:59
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    $\begingroup$ This is in contrast to electromagnetic radiation, which occurs when the charge distribution has a time varying dipole moment That's the condition for dipole radiation. You can have radiation without a changing dipole moment, e.g., quadrupole radiation. $\endgroup$ – Ben Crowell Oct 3 '14 at 0:59
  • $\begingroup$ An accelerated charge always has a changing dipole moment, so all accelerating (classical) charges radiate electromagnetically. This point turns out to be quite subtle, and your statement is not necessarily true. See physics.stackexchange.com/questions/70915/… $\endgroup$ – Ben Crowell Oct 3 '14 at 1:00
  • $\begingroup$ @BenCromwell: What has been observed is that binary pulsars are losing energy and angular momentum commensurate with the prediction of GR. That they are losing both trough gravitational waves is a conjecture, as such waves have not been observed. A fine but important difference, which is very likely going to earn someone a Nobel price in physics within the next couple decades. $\endgroup$ – CuriousOne Oct 3 '14 at 1:51
  • $\begingroup$ @BenCrowell Thanks for the comments. I'm aware of the pulsar measurements, though it's true I've occasionally understated their importance. In this case though, if it were to turn out that GR is wrong (admittedly a poor bet), there is nothing saying that the pulsars need have emitted gravity waves. We still lack a direct detection. As for the other comments, thanks, I'll brush up on my somewhat rusty E&M and correct/clarify a bit. $\endgroup$ – Kyle Oman Oct 3 '14 at 2:02

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